Question

find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x, y) point. y = 5x² + 20x + 35

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). Here, \( a = 5 \), \( b = 20 \), and \( c = 35 \).

Step2: Calculate x - coordinate of vertex

Substitute \( a = 5 \) and \( b = 20 \) into the formula \( x=-\frac{b}{2a} \). We get \( x =-\frac{20}{2\times5}=-\frac{20}{10}=- 2 \).

Step3: Calculate y - coordinate of vertex

Substitute \( x=-2 \) into the equation \( y = 5x^2+20x + 35 \). Then \( y=5\times(-2)^2+20\times(-2)+35=5\times4-40 + 35=20-40 + 35=15 \).

Answer:

\((-2,15)\)